Method and arrangement for generating soft bit information in a receiver of a multiple antenna system

ABSTRACT

The invention which relates to a method and to an arrangement for generating soft bit information in a receiver of a multiple antenna system is based on the object of reducing the calculation complexity for generating the soft bit information. In terms of the method, the object is achieved by virtue of the fact that the iterative deepening search for the Mh antenna is carried out in two substeps, in which case, in the first substep, when the last element of s is not assigned to the mth antenna, s is rotated in such a manner that m is associated with the last element of s, that the channel matrix H is likewise rotated and QR decomposition of the channel matrix H is carried out, that, in the second substep, the iterative deepening search is carried out using a search radius in the form of a vector (Formula (I)); in which (Formula (II)) denotes the number of bit positions in the mth antenna, that the comparison (Formula (III))≧d 2  is carried out for a search radius vector (Formula (IV)) and the search radius is adapted by setting the vector element (Formula (IV)) ( . . . ) of the search vector (Formula (IV)) to the value of the Euclidean distance corresponding to the condition satisfied, that the iterative deepening search is carried out as long as at least one search radius (Formula (IV)) ( . . . ) from the radius vector (Formula (IV)) satisfies the condition (Formula (m))≧d 2  or the comparisons with all of the transmission symbols s(m) of all N Tx  antennas have been carried out, that the soft bit information (Formula (V)) for the antenna m is output, and that the substeps of the method are run through again until all of the soft bit information (Formula (V)) has been determined for all N Tx  antennas.

The invention relates to a method for generating soft bit information ina receiver of a multiple antenna system, in which soft bit informationρ_(k) ^(m), where k=(1, 2, . . . , N_(bits) ^(m)), where N_(bits) ^(m)specifies the number of bit positions in a symbol determined by themodulation and m specifies the number of a transmitting antenna, isformed from a reception vector y using a value set Q of possibletransmission symbols.

The invention also relates to an arrangement for implementing the methodfor generating soft bit information in a receiver of a multiple antennasystem.

In multiple input—multiple output communication systems (MIMO), thetransmission model in the frequency domain can be described using anN_(Rx) dimensional reception vector y, where y=[y₁, . . . , y_(N) _(Rx)]^(T), and an N_(Tx) dimensional transmission vector s, where s=[s(1), .. . , s(N_(Tx))]^(T).

In this case, N_(Rx) is used to denote the number of receiving antennasused and N_(Tx) is used to denote the number of transmitting antennasused.

The parts of s(m) which are contained in s thus correspond, for example,to the complex QAM symbol which is sent on the basis of QAM modulationQ^(m) which is used for a particular transmitting antenna m.

The channel matrix H with the complex elements H(n,m) describes thetransmission behavior between the transmitting and receiving antennas,where H(n,m) represents the transfer function from the mth transmittingantenna to the nth receiving antenna. Therefore, H is an N_(Rx)×N_(Tx)matrix.

The system model can be described by

y=Hs+n   (1)

where n=[n(1), . . . , n(N_(Rx))]^(T) is an N_(Rx) dimensionaluncorrelated noise vector which takes into account the interferenceinfluence caused by the noise in each receiving antenna.

The prior art distinguishes between the methods for the hard decisionand soft decision decoding of the received information.

For a hard decision receiver concept, it is necessary to find thosesymbol vectors s_(min) which were transmitted with the highest degree ofprobability.

For this purpose, the Euclidean distances

d ² =∥y−Hs∥ ²   (2)

are taken into account, the symbol vector s_(min) sought being found bymeans of a minimum search within the values calculated for d².

$\begin{matrix}{s_{\min} = {\arg \mspace{11mu} {\min\limits_{s \in Q}\left\{ {{y - {Hs}}}^{2} \right\}}}} & (3)\end{matrix}$

The notation s ∈ Q is used to show that s_(min) is selected from the setof all possible symbol vectors—the so-called set of symbols Q.

Consequently, the number of all possible symbol vectors |Q| isdetermined by the number of all possible QAM symbols |Q^(m)| for eachtransmitting antenna m using the following equation:

$\begin{matrix}{{Q} = {\prod\limits_{m = 0}^{N_{Tx}}\; {Q^{m}}}} & (4)\end{matrix}$

As soon as the symbol vector s_(min) has been determined, the receivedbits are determined in accordance with the method of a hard decisionreceiver and can thus assume only the value 0 or 1 in accordance withthe binary pattern b(m)=└b^(m)(1), . . . , b^(m)(N_(bit) ^(m))┘ for eachelement s_(min)(m) of s_(min).

In order to make full use of the resources of a channel decoder, forexample a Viterbi decoder, the received bits should not have the valuesof 0 or 1 which are conventional in accordance with a hard decision.

When BPSK modulation is used, for example, a hard decision provides a 0or 1 or −1 or 1 and thus a decision on the mathematical sign. Incontrast, apart from the mathematical sign, a soft decision additionallyprovides information regarding the distance between the value which hasbeen decided and the decision threshold.

It is thus more advantageous to calculate this so-called soft bitinformation ρ_(k) ^(m) (log-likelihood ratio, LLR).

For the kth bit which is transmitted using the mth transmitting antenna,the value of the soft bit information can be given by

$\begin{matrix}{\rho_{k}^{m} = {{\min\limits_{s \in Q_{k}^{m}}\left\{ {{y - {Hs}}}^{2} \right\}} - {\underset{s \in Q_{k}^{m}}{m\underset{\_}{in}}\left\{ {{y - {Hs}}}^{2} \right\}}}} & (5)\end{matrix}$

In this equation (5), two selected partial value sets Q_(k) ^(m) andQ_(k) ^(m) are determined from a value set Q of possible transmissionvectors s ∈ Q.

The partial value set Q_(k) ^(m) comprises those possible transmissionvectors s ∈ Q_(k) ^(m) whose respective element s(m) is assigned abinary pattern b(m) in such a manner that there is a 1 at a kth bitposition of an mth transmitting antenna.

It is thus true for the complementary partial value set Q_(k) ^(m) thatit describes those possible transmission vectors s ∈ Q_(k) ^(m) whichare assigned a 0 at a kth bit position of an mth transmitting antenna.

The number of symbol vectors |Q_(k) ^(m)| and | Q_(k) ^(m) | containedin Q_(k) ^(m) and Q_(k) ^(m) is thus

$\begin{matrix}{{Q_{k}^{m}} = {{\overset{\_}{Q_{k}^{m}}} = {\frac{1}{2}{Q}}}} & (6)\end{matrix}$

An algorithm for sphere decoding is disclosed, for example, in “A newReduced-Complexity Sphere Decoder For Multiple Antenna Systems”, AlbertM. Chan, Inkyu Lee, 2002 IEEE, “On the Sphere Decoding Algorithm I.Expected Complexity”, B. Hassibi, H. Vikalo, IEEE Transactions on SignalProcessing, vol. 53, no. 8, pp. 2806-2818, August 2005 and in “VLSIImplementation of MIMO Detection Using the Sphere Decoding Algorithm”,A. Burg, M. Borgmann, M. Wenk, M. Zellweger, IEEE Journal of Solid StateCircuits, vol. 40, no. 7, July 2005.

These methods according to the prior art can be used to solve equation(3), to determine the shortest Euclidean distance and thus to ascertainthe symbol vector s_(min) which was transmitted with the greatest degreeof probability.

These approaches are thus used for sphere decoding for a hard decisionreceiver concept.

For this purpose, QR decomposition of the channel matrix H is carriedout, Q representing a Hermitian matrix, where Q⁻¹=Q^(T), and Rrepresenting the upper triangular matrix.

Equation (2) can therefore be expressed by

$\begin{matrix}\begin{matrix}{d^{2} = {{{y - {Hs}}}^{2} = {{y - {QRs}}}^{2}}} \\{= {{Q\left( {\hat{y} - {Rs}} \right)}}^{2}} \\{= {{\hat{y} - {Rs}}}^{2}}\end{matrix} & (7)\end{matrix}$

where

ŷ=Q ⁻¹ y   (8)

Since the matrix Q represents only a Hermitian rotation matrix, it canbe ignored for the distance calculation. On account of the triangularstructure of the R matrix in the upper region, the Euclidean distance d²can be divided, in accordance with equation (7) and within the number oftransmitting antennas N_(Tx), into Euclidean partial distances d_(m) ²which can be represented in a tree structure.

Such a search tree comprises a number of levels corresponding to thenumber of transmitting antennas N_(Tx), each level l being assigned acorresponding transmitting antenna m using I =N_(Tx)−m+1. Subsequentnodes which correspond to the possible QAM symbols s(m) ∈ Q^(m) from theset of symbols are inserted on each level l, the number of subsequentnodes |Q^(m)| being prescribed by the type of modulation in atransmitting antenna m.

FIG. 1 illustrates an example with N_(Tx)=3, N_(Rx)=3 and QPSK type ofmodulation for all transmitting antennas. This shows that the QAMsymbols s(3) are on the uppermost level, while the elements s(1) arearranged on the lowermost level of the tree structure.

It is furthermore assumed that the subsequent nodes which are assignedto the same predecessor node are arranged in such a manner that thecorresponding Euclidean partial distances d_(m) ² increase from left toright, as is likewise illustrated in FIG. 1.

$\begin{matrix}{{d^{2} = {{{\begin{pmatrix}{\hat{y}(1)} \\{\hat{y}(2)} \\{\hat{y}(3)}\end{pmatrix} - {\begin{pmatrix}{r\left( {1,1} \right)} & {r\left( {1,2} \right)} & {r\left( {1,3} \right)} \\0 & {r\left( {2,2} \right)} & {r\left( {2,3} \right)} \\0 & 0 & {r\left( {3,3} \right)}\end{pmatrix}\begin{pmatrix}{s(1)} \\{s(2)} \\{s(3)}\end{pmatrix}}}}^{2} = \begin{matrix}\left. \rightarrow d_{1}^{2} \right. \\\left. \rightarrow d_{2}^{2} \right. \\\left. \rightarrow d_{3}^{2} \right.\end{matrix}}}{d^{2} = {d_{1}^{2} + d_{2}^{2} + d_{3}^{2}}}} & (9)\end{matrix}$

In order to find the symbol vector s_(min) which was sent with thehighest degree of probability and for which the Euclidean distanceaccording to equation (7) is thus minimal, a maximum sphere radiusr_(max) ² is selected in such a manner that the symbol vector s_(min) isreliably contained in said sphere radius.

FIG. 2 shows an example of such a deepening search for N_(Tx)=3,N_(Rx)=3 and QPSK modulation for all transmitting antennas. The searchpointer runs down through the tree structure to the lower level as longas the sphere constraints

$\begin{matrix}{{{sphere}\mspace{14mu} {constraint}} = \left\{ \begin{matrix}{r_{\max}^{2} \geq d_{3}^{2}} & {{{for}\mspace{14mu} {level}{\mspace{11mu} \;}l} = 1} \\{r_{\max}^{2} \geq {d_{2}^{2} + d_{3}^{2}}} & {{{for}{\mspace{11mu} \;}{level}\mspace{14mu} l} = 2} \\{r_{\max}^{2} \geq {d_{1}^{2} + d_{2}^{2} + d_{3}^{2}}} & {{{for}\mspace{14mu} {level}\mspace{14mu} l} = 3}\end{matrix} \right.} & (10)\end{matrix}$

are met for each level.

If the sphere constraint condition is no longer satisfied at aparticular node of a level l, the next node arranged on the level lwould likewise not satisfy the sphere constraint condition on account ofthe arrangement of the subsequent nodes and the search is continued atthe level l-1. As soon as the search reaches the lowermost level, themaximum sphere radius r_(max) ² is updated in accordance with theformula

r _(max) ² =d ₁ ² +d ₂ ² +d ₃ ²   11)

and the symbol vector s_(min) is assumed in accordance with the searchpath.

According to the prior art, the method described below is known for asoft decision sphere decoder.

The number of bits sent using the mth transmitting antenna is given, forexample, by N_(bits) ^(m).

The total number of bits transmitted using all of the transmittingantennas is thus

$\begin{matrix}{N_{bits} = {\sum\limits_{m = 1}^{N_{Tx}}N_{bits}^{m}}} & (12)\end{matrix}$

As shown in formula (5), two minimum Euclidean distances must bedetermined in order to calculate one soft bit ρ_(k) ^(m), with theresult that, in total, 2*N_(bits) transmission vectors s_(min) must befound in order to be able to state all ρ_(k) ^(m).

For the abovementioned example with N_(Tx)=3, N_(Rx)=3 and QPSKmodulation, this means, for example, that a total of 4 transmissionvectors s_(min) according to (3), but with s_(min) ∈ Q₁ ¹, s_(min) ∈ Q₁¹ , s_(min) ∈ Q₂ ¹ and s_(min) ∈ Q₂ ¹ , have to be found in order tocalculate ρ_(k) ^(m) for the first transmitting antenna m=1. 4transmission vectors s_(min) likewise need to be respectively determinedfor all further transmitting antennas, as shown in the followingequation:

$\begin{matrix}{\left. \begin{pmatrix}\rho_{1}^{1} & \rho_{2}^{1} \\\rho_{1}^{2} & \rho_{2}^{2} \\\rho_{1}^{3} & \rho_{2}^{3}\end{pmatrix}\rightarrow s_{\min} \right. \in \begin{pmatrix}Q_{1}^{1} & \overset{\_}{Q_{1}^{1}} & Q_{2}^{1} & \overset{\_}{Q_{2}^{1}} \\Q_{1}^{2} & \overset{\_}{Q_{1}^{2}} & Q_{2}^{2} & \overset{\_}{Q_{2}^{2}} \\Q_{1}^{3} & \overset{\_}{Q_{1}^{3}} & Q_{2}^{3} & \overset{\_}{Q_{1}^{3}}\end{pmatrix}} & (13)\end{matrix}$

The sphere decoder (LSD, list sphere decoding) described in ApproachingMIMO Channel Capacity With Soft Detection Based on Hard Sphere Decoding,Renqiu Wang, Georgios B. Giannakis, WCNC 2004/IEEE Communication Societyis based on a hard decision sphere decoder for calculating the soft bitsand for solving equation (5).

N_(bits)+1 deepening search runs are required for this purpose, eachdeepening search being carried out with a search tree whose structurehas been changed.

A transmission vector s_(min) is first of all determined using a harddecision decoder, as already described further above. Since thistransmission vector is s_(min) ∈ Q, it can also be associated withs_(min) ∈ Q_(k) ^(m) and s_(min) ∈ Q_(k) ^(m) , as shall be explainedbelow for each antenna m and each bit k using an example.

If the transmission vector s_(min) is determined in accordance withequation (3), the next transmission vector, taking into account allpossibilities for s ∈ Q, is, for example

$\begin{matrix}{s_{\min} = {\begin{pmatrix}{s_{\min}(1)} \\{s_{\min}(2)} \\{s_{\min}(3)}\end{pmatrix} = {\left. \begin{pmatrix}{1 + j} \\{1 - j} \\{{- 1} + j}\end{pmatrix}\rightarrow\begin{pmatrix}{b(1)} \\{b(2)} \\{b(3)}\end{pmatrix} \right. = \begin{pmatrix}11 \\10 \\01\end{pmatrix}}}} & (14)\end{matrix}$

where b(1)=[11] expresses the bit pattern associated with s_(min)(1).

The symbol vector s_(min) is thus likewise the next symbol vector forthe following subsets:

$\begin{matrix}{s_{\min} \in \left. \begin{pmatrix}Q_{1}^{1} & Q_{2}^{1} \\Q_{1}^{2} & \overset{\_}{Q_{2}^{2}} \\\overset{\_}{Q_{1}^{3}} & Q_{2}^{2}\end{pmatrix}\rightarrow{1\mspace{14mu} {deepening}\mspace{14mu} {search}} \right.} & (15)\end{matrix}$

Therefore, for the example given, the next symbol vector s_(min) muststill be found for the complementary subset:

$\underset{N_{bits}{deepening}\mspace{14mu} {searches}}{\underset{}{\begin{matrix}{{s_{\min} \in \overset{\_}{Q_{1}^{1}}},{s_{\min} \in \overset{\_}{Q_{2}^{1}}},{s_{\min} \in \overset{\_}{Q_{1}^{2}}},} \\{{s_{\min} \in Q_{2}^{2}},{s_{\min} \in Q_{1}^{3}},{{{and}\mspace{14mu} s_{\min}} \in Q_{2}^{2}},}\end{matrix}}}$

In addition to this initial first deepening search, further N_(bits)deepening searches must therefore subsequently be carried out. However,each further deepening search respectively requires a modification tothe search tree illustrated in FIG. 2 in order to find the symbol vectors_(min) ∈ Q_(k) ^(m) or s_(min) ∈ Q_(k) ^(m) .

Since Q_(k) ^(m) or Q_(k) ^(m) each only has ½|Q| possible transmissionsymbol vectors s, the number of subsequent nodes on the lth level of thetree (l=N_(Tx)−m+1) is respectively halved. One disadvantage of thissolution according to the prior art is thus that this method requiresN_(bits)+1 deepening searches in order to calculate the soft bits forall of the bits sent using N_(Tx) transmitting antennas. A furtherdisadvantage is that the individual searches are highly redundant sincethe search trees at least partially overlap.

The object of the invention is thus to specify a method and anarrangement for generating soft bit information in a receiver of amultiple antenna system, which is used to reduce the calculationcomplexity for generating the soft bit information.

In terms of the method, the object is achieved, according to theinvention, by virtue of the fact that the iterative deepening search forthe mth antenna is carried out in two substeps, in which case, in thefirst substep, when the last element of s is not assigned to the mthantenna, s is rotated in such a manner that m is associated with thelast element of s, that the channel matrix H is likewise rotated and QRdecomposition of the channel matrix H is carried out, that, in thesecond substep, the iterative deepening search is carried out using asearch radius in the form of a vector r_(max) ²=└r_(max) ²(Q₁ ^(m)),r_(max) ²( Q₁ ^(m) ), . . . , r_(max) ²(Q_(N) _(bits) _(m) ^(m)),r_(max) ²(Q_(N) _(bits) _(m) ^(m))┘, in which N_(bits) ^(m) denotes thenumber of bit positions in the mth antenna, that the comparison └r_(max)²( . . . ), r_(max) ²( . . . )┘≧d² is carried out for a search radiusvector r_(max) ² and the search radius is adapted by setting the vectorelement r_(max) ²( . . . ) of the search radius vector r_(max) ² to thevalue of the Euclidean distance corresponding to the conditionsatisfied, that the iterative deepening search is carried out as long asat least one search radius r_(max) ²( . . . ) from the radius vectorr_(max) ² satisfies the condition └r_(max) ²( . . . ), r_(max) ²( . . .)┘≧d² or the comparisons with all of the transmission symbols s(m) ofall N_(Tx) antennas have been carried out, that the soft bit informationρ_(k) ^(m) for the antenna m is output, and that the substeps of themethod are run through again until all of the soft bit information ρ_(k)^(m) has been determined for all N_(Tx) antennas.

In contrast to the prior art, the inventive iterative deepening searchis carried out in two sub steps.

The first substep checks whether the last element of s is assigned tothe mth antenna. If this is the case, the method continues with thesecond substep.

The inventive deepening search preferably begins with the search fors_(min) ∈ Q_(k) ^(m) or s_(min) ∈ Q_(k) ^(m) (for all k), m being thelast element s(N_(Tx)) of the transmission vector s. Consequently, allsoft bits ρ_(k) ^(m) can be calculated for m=N_(Tx) in accordance withthe deepening search.

If the last element of s is not assigned to the mth transmittingantenna, s is rotated in such a manner that m is associated with thelast element of s; the channel matrix H is also concomitantly rotated inthis case. QR decomposition of the channel matrix H is then required.

In the second substep, the actual iterative deepening search is thencarried out using a search radius in the form of a vector r_(max)²=└r_(max) ²(Q₁ ^(m)), r_(max) ²( Q₁ ^(m) ), . . . r_(max) ²(Q_(N)_(bits) _(m) ^(m)), r_(max) ²( Q_(N) _(bits) _(m) ^(m) )┘]. This searchradius vector r_(max) ² comprises a plurality of search radii r_(max) ²(. . . ) which are each assigned to the individual deepening searchess_(min) ∈ Q_(k) ^(m) and s_(min) ∈ Q_(k) ^(m) which are assigned to thetransmitting antenna m=N_(Tx). During the deepening search, a total ofN_(bits) ^(m) individual search radii r_(max) ²( . . . ) are taken fromthe radius vector r_(max) ²ax and combined to form a multiple sphereconstraint. This multiple sphere constraint is always reformed duringthe deepening search as soon as the search reaches the uppermost levell=1 of the search tree. In this case, the bit pattern b(m) assigned to aQAM symbol s(m) on level l=1 is taken into account. The radius r_(max)²(Q_(k) ^(m)) can then be selected for each of the elements of b(m)=└b₁^(m), b₂ ^(m), . . . , b_(N) _(bits) _(m) ^(m)┘, if b_(k) ^(m)=1, orr_(max) ²( Q_(k) ^(m) ) is selected if b_(k) ^(m)=0.

In this respect, FIG. 3 shows one example of the selection of themultiple sphere constraint └r_(max) ²( . . . ), r_(max) ²( . . . )┘ forN_(Tx)=N_(Rx)=3 and QPSK.

The iterative deepening search is carried out according to the samescheme as the deepening search in FIG. 2. However, instead of anindividual sphere constraint, use is now made of a multiple sphereconstraint comprising a total of N_(bits) ^(m) individual search radii.The Euclidean partial distances d₁ ², d₂ ² and d₃ ² likewise correspondto those from equation (9). However, so that the deepening search shownin FIG. 3 can be continued downward, it is necessary to check themultiple sphere constraint which is met as soon as at least one elementof the multiple sphere constraint [r_(max) ²( . . . ), r_(max) ²( . . .)] is ≧d₁ ², d₁ ²+d₂ ² or d₁ ²+d₂ ²+d₃ ², depending on the level l, asillustrated in FIG. 3. If none of the radii contained in the multiplesphere constraint satisfies the above requirement, the search must becontinued further at level l-1. At the lowest level l=N_(Tx), allr_(max) ²(Q_(k) ^(m)) or r_(max) ²( Q_(k) ^(m) ) from the selectedsphere constraint may now be adapted according to equation (11) as longas it is actually a minimization of r_(max) ²(Q_(k) ^(m)) or r_(max) ²(Q_(k) ^(m) ). In this case, the current symbol vector is also stored asthe result of the search for s_(min) ∈ Q_(k) ^(m) or s_(min) ∈ Q_(k)^(m) in accordance with the search path.

If, during the further deepening search, the level l=1 is reached again,a new multiple sphere constraint is selected, as illustrated in FIG. 3.

The deepening search just described is continued until either the entiresearch tree has been passed through or the following terminationcriterion T has been satisfied. If the condition r_(max) ²(Q_(k)^(m))≧d₃ ² or r_(max) ²( Q_(k) ^(m) )≧d₃ ² is not satisfied for anindividual radius from the multiple sphere constraint └r_(max) ²( . . .), r_(max) ²( . . . )┘ at the level l=1, the search for s_(min) ∈ Q_(k)^(m) or s_(min) ∈ Q_(k) ^(m) can be considered to be concluded. Thetermination criterion T is consequently satisfied when all of thesearches for s_(min) ∈ Q_(k) ^(m) or s_(min) ∈ Q_(k) ^(m) have alreadybeen considered to be concluded.

All s_(min) ∈ Q_(k) ^(m) or s_(min) ∈ Q_(k) ^(m) for all k but only form=N_(Tx) are output as the result of the deepening search justdescribed. Consequently, all soft bits ρ_(k) ^(m) for the transmittingantenna m=N_(Tx) can also be calculated after the deepening search hasbeen concluded.

In order to calculate the soft bits for m≠N_(Tx) and to carry out thecorresponding search for s_(min), the transmission vector s must berotated (Tx rotation) before the described deepening search. If, forexample, all ρ_(k) ^(m) are intended to be calculated for m=N_(Tx)−1,the elements of s=[s(1), . . . , s(N_(Tx)−1), s(N_(Tx))]^(T) must becyclically rotated once s_(rot)=[s(N_(Tx)), s(1), . . . ,s(N_(Tx)−1)]^(T) for this purpose such that the elements s(N_(Tx)−1) cannow be found at the last position within s and thus at the uppermostlevel l=1 of the search tree. However, such a Tx rotation likewiseentails a cyclic rotation of the column vectors of H, which thussignifies another QR decomposition. The following equation illustratesthis method:

$\begin{matrix}{d^{2} = {{\underset{{{without}\mspace{14mu} {Tx}\mspace{14mu} {rotation}\mspace{14mu} {in}\mspace{14mu} {order}\mspace{14mu} {to}}{{{calculate}\mspace{14mu} \rho_{k}^{m}{for}\mspace{14mu} m} = {3{({m = N_{Tx}})}}}}{\underset{}{{y - {\left( {h_{1},h_{2},h_{3}} \right)\begin{pmatrix}{s(1)} \\{s(2)} \\{s(3)}\end{pmatrix}}}}}}^{2} = {\underset{{{with}\mspace{14mu} {Tx}\mspace{14mu} {rotation}\mspace{14mu} {in}\mspace{14mu} {order}\mspace{14mu} {to}}\mspace{56mu} {{{calculate}\mspace{14mu} \rho_{k}^{m}{for}\mspace{14mu} m} = {2{({m = {N_{Tx} - 1}})}}}}{\underset{}{{y - {\left( {h_{3},h_{1},h_{2}} \right)\begin{pmatrix}{s(3)} \\{s(1)} \\{s(2)}\end{pmatrix}}}}}}^{2}}} & (16)\end{matrix}$

If such a Tx rotation including another QR decomposition of the channelmatrix H is therefore carried out, the deepening search described can beused to calculate all further soft bits for m=N_(Tx)−1, for example.

The method with its substeps is run through again until the soft bitinformation ρ_(k) ^(m) has been determined and output for all N_(Tx)transmitting antennas.

In this respect, FIG. 4 shows a suitable arrangement. In said figure, ris called the reception vector y and ŷ=Q⁻¹·r. In addition, H⁰ signifiesthe channel matrix which has not been rotated and is used as a basis forcalculating ρ_(k) ^(m) for m=N_(Tx), whereas H^(N) ^(Tx) ⁻¹ denotes thatversion of the channel matrix H which has been cyclically rotated(N_(Tx)−1) times and can be used to determine ρ_(k) ^(m) for m=1.

One embodiment of the invention provides for the iterative deepeningsearch to be terminated before all of the soft bit information ρ_(k)^(m) is determined for all N_(Tx) antennas.

Another embodiment of the invention provides for the iterative deepeningsearch to be terminated after a prescribed number of search steps hasbeen reached.

For example, prescribing a number of search steps makes it possible forthe inventive method for generating soft bit information to be possiblyterminated prematurely, that is to say not all of the search stepsneeded to search a search tree completely are implemented. If the methodhas not already been terminated before the prescribed number of searchsteps because, for example, the soft bit information has already beendetermined and output, the deepening search is terminated when theprescribed number of search steps is reached. On the one hand, thisspeeds up the search method but it may result in a greater degree ofinaccuracy of the soft bit information as a result of prematuretermination. Other criteria for prematurely terminating the searchmethod are likewise possible.

In terms of the arrangement, the object is achieved, according to theinvention, by virtue of the fact that a QR decomposition arrangement fordecomposing the QR matrix is connected downstream of a Tx rotationarrangement which is intended to rotate s and H and has an input for aninput signal y, that an output of the QR decomposition arrangement isconnected to an input of a deepening search arrangement, that thedeepening search arrangement has two outputs which are intended tooutput s_(min) ∈ Q_(k) ^(m=N) ^(Tx) and s_(min) ∈ Q_(k) ^(m=N) ^(Tx) andare each connected to an input of a summing arrangement, and that thesumming arrangement has an output for outputting an item of soft bitinformation ρ_(k) ^(m).

The vector s, and thus also the channel matrix H, are rotated asrequired by the invention in the Tx rotation arrangement for rotating sand H. The requisite number of rotations is determined by the number ofexisting transmitting antennas N_(Tx) since a deepening search must becarried out for each existing transmitting antenna. In the QRdecomposition arrangement which is connected downstream of the Txrotation arrangement, the channel matrix H is decomposed into the Qmatrix and the R matrix, as already described.

The iterative deepening search for an mth antenna is carried out in thedownstream deepening search arrangement using the inventive searchradius r_(max) ² in the form of a vector.

As a result of this deepening search, two minima, namely s_(min) ∈ Q_(k)^(m−N) ^(Tx) and s_(min) ∈ Q_(k) ^(m−N) ^(Tx) , are output and aresubtracted in the downstream summing arrangement in accordance withequation (5).

This difference is output as the soft bit information ρ_(k) ^(m) of themth antenna.

One particular embodiment of the invention provides for a plurality ofseries circuits comprising a QR decomposition arrangement, a deepeningsearch arrangement and a summing arrangement to be connected downstreamof the Tx rotation arrangement in a parallel manner.

This arrangement makes it possible to calculate the soft bits in aparallel manner, which makes it possible to speed up determination ofthe soft bit information ρ_(k) ^(m). In this case, it is possible toconnect two or more such series circuits downstream of the Tx rotationarrangement. In one particular case, the number of series circuitscorresponds to the number of transmitting antennas N_(Tx).

The invention shall be explained in more detail below with reference toan exemplary embodiment. In the associated drawings:

FIG. 1 shows a tree structure of a search tree from the prior art for anexample with N_(Tx)=3, N_(Rx)=3 and QPSK modulation,

FIG. 2 shows an example of an iterative deepening search using a spheredecoder from the prior art with N_(Tx)=3, N_(Rx)=3 and QPSK modulation,

FIG. 3 shows an example of an inventive deepening search using theinventive search radius r_(max) ² in the form of a vector,

FIG. 4 shows an inventive arrangement for implementing the method, and

FIG. 5 shows an example of reducing the multiple sphere constraintcondition while running through the method in accordance with theinvention.

The following paragraph describes the inventive approach for a softdecision sphere decoder, which results in a significant reduction in thecalculation complexity by introducing the inventive search radiusr_(max) ² in the form of a vector. This search radius vector r_(max) ²is used to implement a search with a plurality of search radii (multipleradius search). The method also rotates the reception vector y (Txrotation).

Replacing the “single radius search” with a “multiple radius search”makes it possible for the sphere decoder to calculate all of the softbits for a transmitting antenna m=N_(Tx) by running through the methodonce. In order to calculate all of the soft bits of all furthertransmitting antennas m≠N_(Tx), a further inventive method step is used,the so-called “Tx rotation”.

The inventive method for a soft decision sphere decoder likewiserequires QR decomposition of the channel matrix H during a preparatorymethod step. This has already been represented in equation (7). Thesearch tree for the inventive solution is also comparable to thatillustrated in FIG. 2 for a “hard decision sphere decoder”.

Instead of a single maximum sphere radius r_(max) ², the inventivesearch radius

r _(max) ² =└r _(max) ²(Q ₁ ^(m)), r _(max) ²( Q ₁ ^(m) ), . . . r_(max) ²(Q _(N) _(bits) _(m) ^(m)), r _(max) ²( Q _(N) _(bits) _(m) ^(m))┘  (17)

in the form of a vector is used to determine the soft bit informationρ_(k) ^(m).

Each element r_(max) ²(Q₁ ^(m)) or r²( Q_(k) ^(m) ) corresponds to themaximum sphere radius for the depth-oriented search method fordetermining s_(min) ∈ Q_(k) ^(m) and s_(min) ∈ Q_(k) ^(m) .

The depth-oriented search method for this method is carried out in themanner already described further above.

However, a first difference in the inventive method is that, inaccordance with the bit pattern b(N_(Tx)) assigned to each elements(N_(Tx)) on the uppermost level of the tree structure, a maximum ofN_(bits) ^(m)(m=N_(Tx)) individual elements are selected from the searchradius vector r_(max) ² (a multiple sphere constraint) for the inventivedeepening search and are combined to form a multiple sphere constraint.

The multiple sphere constraint condition of such a deepening search isthen satisfied if at least one element r_(max) ²( . . . ) from themultiple sphere constraint condition satisfies the inequality accordingto equation (10) or, in other words, the multiple sphere constraintcondition is not satisfied if none of its elements r_(max) ²( . . . )satisfies equation (10).

Therefore, the deepening search runs through the tree structure from thetop downward as long as at least one element r_(max) ²( . . . ) from themultiple sphere constraint condition satisfies equation (10) and doesnot exceed the corresponding partial Euclidean distances.

Accordingly, the search pointer moves down one level when the multiplesphere constraint condition has been satisfied.

If the multiple sphere constraint condition cannot be satisfied, thesearch is continued further one level up.

The deepening search using the radius vector r_(max) ² is thus used tofind s_(min) ∈ Q_(k) ^(m) and s_(min) ∈ Q_(k) ^(m) by means of themethod for generating soft bit information.

FIG. 3 illustrates this sequence using the example of N_(Tx)=3, N_(Rx)=3and QPSK modulation for all transmitting antennas.

During the inventive deepening search for finding individual s_(min) ∈Q_(k) ^(m) and s_(min) ∈ Q_(k) ^(m) , it is possible to reduce themultiple sphere constraint condition └r_(max) ²( . . . ), . . . ,r_(max) ²( . . . )┘.

FIG. 5 shows this behavior using the example of a 16-QAM type ofmodulation. When one of the elements r_(max) ²(Q_(k) ^(m)) or r_(max) ²(Q_(k) ^(m) ) from the multiple sphere constraint condition cannotsatisfy equation (10) at the uppermost level l=1 of the tree structure,the respective search for s_(min) ∈ Q_(k) ^(m) or s_(min) ∈ Q_(k) ^(m)can be considered to be concluded and r_(max) ²( Q_(k) ^(m) ) or r_(max)²( Q_(k) ^(m) ) can be deleted from the multiple sphere constraintcondition for the deepening search according to the method.

The above example of FIG. 5 shows that r_(max) ²( Q_(k=1) ^(m) )≧d₃ ²cannot be satisfied. Assuming (already described in FIG. 1) that theelements are arranged in the search tree in such a manner that d₃ ²increase from left to right, an element s(m) ∈ Q_(k=1) ^(m) , which isarranged further to the right, can no longer reliably satisfy the abovecondition r_(max) ²( Q_(k=1) ^(m) )≧d₃ ² either.

The multiple sphere constraint condition can thus be reduced by theindividual radius r_(max) ²( Q_(k=1) ^(m) ) for all subsequent deepeningsearch steps.

The number of elements in the multiple sphere constraint condition isthus reduced. It is obvious that the deepening search can then only becontinued further as long as the multiple sphere constraint conditioncomprises at least one radius.

As soon as the deepening search using the search radius vector r_(max) ²has been concluded, all of the nearest symbol vectors s_(min) ∈ Q_(k)^(m) and s_(min) ∈ Q_(k) ^(m) for the last transmitting antenna m=N_(Tx)are found.

The determination of the corresponding symbol vector s_(min) for theremaining transmitting antennas m≠N_(Tx) and the calculation of thecorresponding soft bits ρ_(k) ^(m) are carried out as described below.

As already explained, the introduction of a search using a multiplesphere constraint condition means that all soft bit information ρ_(k)^(m) is calculated only for the transmitting antenna m=N_(Tx).

In order to calculate the soft bit information ρ_(k) ^(m) for an antennam≠N_(Tx), the symbol vector s can be cyclically rotated, with the resultthat each element s(m) respectively appears once at the last positionwithin s.

For the example with N_(Tx)=3, N_(Rx)=3, the Euclidean distance can bedescribed in accordance with equation (2) as follows

$\begin{matrix}{d^{2} = {\underset{{{without}\mspace{14mu} {Tx}\mspace{14mu} {rotation}\mspace{14mu} {in}\mspace{14mu} {order}\mspace{14mu} {to}}{{{calculate}\mspace{14mu} \rho_{k}^{m}{for}\mspace{14mu} m} = {3{({m = N_{Tx}})}}}}{\underset{}{{y - {\left( {h_{1},h_{2},h_{3}} \right)\begin{pmatrix}{s(1)} \\{s(2)} \\{s(3)}\end{pmatrix}}}}}}^{2}} \\{= {\underset{{{with}\mspace{14mu} {Tx}\mspace{14mu} {rotation}\mspace{14mu} {in}\mspace{14mu} {order}\mspace{14mu} {to}}\mspace{56mu} {{{calculate}\mspace{14mu} \rho_{k}^{m}{for}\mspace{14mu} m} = {2{({m = {N_{Tx} - 1}})}}}}{\underset{}{{y - {\left( {h_{3},h_{1},h_{2}} \right)\begin{pmatrix}{s(3)} \\{s(1)} \\{s(2)}\end{pmatrix}}}}}}^{2}} \\{= {\underset{{{with}\mspace{14mu} {Tx}\mspace{14mu} {rotation}\mspace{14mu} {in}\mspace{14mu} {order}\mspace{14mu} {to}}\mspace{56mu} {{{calculate}\mspace{14mu} \rho_{k}^{m}{for}\mspace{14mu} m} = {1{({m = {N_{Tx} - 2}})}}}}{\underset{}{{y - {\left( {h_{2},h_{3},h_{1}} \right)\begin{pmatrix}{s(2)} \\{s(3)} \\{s(1)}\end{pmatrix}}}}}}^{2}}\end{matrix}$

where h_(m) is the column vector of the channel matrix H.

Equation (18) shows that, as a result of the rotation of s, each elements(m) is at the last position in the vector s once and therefore appearson the uppermost level l=1 of the tree on which the search for thesymbol vector s_(min) ∈ Q_(k) ^(m) or s_(min) ∈ Q_(k) ^(m) is beingcarried out according to the invention.

However, it can also be seen that the rotation of s results in anequivalent rotation of the column vectors h_(m) of the channel matrixH=└h₁, . . . , h_(N) _(Tx) ┘.

QR decomposition of the rotated channel matrix H⁰, . . . , H^(N) ^(Tx)⁻¹ thus provides different Q and R matrices for each rotation step.

In accordance with the method steps mentioned above, the inventivesphere decoder can be constructed as illustrated in FIG. 4.

In a first stage of a Tx rotation arrangement, the input channel matrixH is rotated according to equation (18). A separate QR decomposition isthen carried out in the QR decomposition arrangement. The inventivedeepening search using the radius vector r_(max) ² is individuallycarried out for each rotation step in the downstream deepening searcharrangement.

The soft bit information ρ_(k) ^(m) for the associated transmittingantenna m can thus be calculated according to equation (5) for eachrotation step and then output.

Achieving the object in this manner requires N_(Tx) search runs in orderto calculate all of the soft bit information ρ_(k) ^(m) for all of thetransmitting antennas.

If the complexity of the sphere decoder (LSD) disclosed in ApproachingMIMO Channel Capacity With Soft Detection Based on Hard Sphere Decoding,Renqiu Wang, Georgios B. Giannakis, WCNC 2004/IEEE Communication Societyis compared with the inventive solution, it is possible to determinethat N_(bits)+1 search runs with only one sphere constraint (searchradius) are required for the LSD sphere decoder. That is to say, thecomplexity of a deepening search is even dependent on the respective QAMmodulation used.

Even if a search using a radius vector r_(max) ² requires greatercalculation complexity than a search with only one sphere constraintcondition r_(max) ², it can be determined that the overall complexity ofthe inventive sphere decoder is lower than in the case of the solutionwhich is known from the prior art and uses an LSD sphere decoder.

1. A method for generating soft bit information in a receiver of amultiple antenna system, in which soft bit information ρ_(k) ^(m) isformed from a reception vector y using a value set ${Q = \begin{pmatrix}Q^{1} \\Q^{m} \\\ldots \\Q^{N_{Tx}}\end{pmatrix}},$ where m=(1, 2, . . . , N_(Tx)) with the number ofN_(Tx) transmitting antennas, of possible transmission symbols Q^(m),with division of the value set Q into partial value sets Q_(k) ^(m) andQ_(k) ^(m) , the partial value set Q_(k) ^(m) describing those possibletransmission vectors s ∈ Q which are assigned a 1 at a kth bit positionof an mth transmitting antenna, and the partial value set Q_(k) ^(m)describing those possible transmission vectors s ∈ Q which are assigneda 0 at a kth bit position of an mth transmitting antenna, where k=(1, 2,. . . , N_(bits) ^(m)), N_(bits) ^(m) specifying the number of bitpositions in a transmission symbol s(m) determined by the modulation andm specifying the number of a transmitting antenna and k representing thekth bit of a possible transmission symbol of the mth antenna s(m), wheres(m) ∈ Q^(m), and the soft bit information ρ_(k) ^(m) is formedaccording to$\rho_{k}^{m} = {{\min\limits_{s \in Q_{k}^{m}}\left\{ {{y - {Hs}}}^{2} \right\}} - {\underset{s \in Q_{k}^{m}}{m\; \underset{\_}{in}}\left\{ {{y - {Hs}}}^{2} \right\}}}$using a channel matrix H, which describes the transmission channelbetween the transmitter and the receiver, and the transmission vector s∈ Q with the possible transmission symbols of the N_(Tx) antennas asvector elements, the Euclidean distance being d²=∥y−Hs∥², the minimum$\min\limits_{s \in Q_{k}^{m}}\left\{ {{y - {Hs}}}^{2} \right\}$ andthe minimum$\underset{s \in Q_{k}^{m}}{m\; \underset{\_}{in}}\left\{ {{y - {Hs}}}^{2} \right\}$of the Euclidean distances d² being determined using an iterativedeepening search with QR decomposition of the channel matrix H using asearch radius r_(max) ² and with adaptation of the search radius r_(max)², wherein the iterative deepening search for the mth antenna is carriedout in two substeps, in which case, in the first substep, when the lastelement of s is not assigned to the mth antenna, s is rotated in such amanner that m is associated with the last element of s, wherein thechannel matrix H is likewise rotated and QR decomposition of the channelmatrix H is carried out, wherein, in the second substep, the iterativedeepening search is carried out using a search radius in the form of avector r_(max) ²=└r_(max) ²(Q₁ ^(m)), r_(max) ²( Q₁ ^(m) ), . . .r_(max) ²((Q _(N) _(bits) _(m) ^(m)), r_(max) ²( Q_(N) _(bits) _(m) ^(m))┘, in which N_(bits) ^(m) denotes the number of bit positions in themth antenna, wherein the comparison └r_(max) ²( . . . ), r_(max) ²( . .. )┘≧d² is carried out for a search radius vector r_(max) ² and thesearch radius is adapted by setting the vector element r_(max) ²( . . .) of the search radius vector r_(max) ² to the value of the Euclideandistance corresponding to the condition satisfied, wherein the iterativedeepening search is carried out as long as at least one search radiusr_(max) ²( . . . ) from the radius vector r_(max) ² satisfies thecondition └r_(max) ²( . . . ), r_(max) ²( . . . )┘≧d² or the comparisonswith all of the transmission symbols s(m) of all N_(Tx) antennas havebeen carried out, wherein the soft bit information ρ_(k) ^(m) for theantenna m is output, and wherein the substeps of the method are runthrough again until all of the soft bit information ρ_(k) ^(m) has beendetermined for all N_(Tx) antennas.
 2. The method as claimed in claim 1,wherein the iterative deepening search is terminated before all of thesoft bit information ρ_(k) ^(m) is determined for all N_(Tx) antennas.3. The method as claimed in claim 2, wherein the iterative deepeningsearch is terminated after a prescribed number of search steps has beenreached.
 4. An arrangement for generating soft bit information in areceiver of a multiple antenna system, wherein a QR decompositionarrangement for decomposing a QR matrix is connected downstream of a Txrotation arrangement which is intended to rotate s and H and has aninput for an input signal y, wherein an output of the QR decompositionarrangement is connected to an input of a deepening search arrangement,wherein the deepening search arrangement has two outputs which areintended to output s_(min) ∈ Q_(k) ^(m=N) ^(Tx) and s_(min) ∈ Q_(k)^(m=N) ^(Tx) and are each connected to an input of a summingarrangement, and wherein the summing arrangement has an output foroutputting an item of soft bit information ρ_(k) ^(m).
 5. Thearrangement as claimed in claim 4, wherein a plurality of seriescircuits comprising a QR decomposition arrangement, a deepening searcharrangement and a summing arrangement are connected downstream of the Txrotation arrangement in a parallel manner.